WASHINGTON, Feb 1 (Reuters) - U.S. factory activity slowed in January amid a fall in new orders, but an unexpected drop in the number of Americans filing for unemployment benefits last week pointed to sustained labor market strength that should underpin domestic demand.

The economy's healthy fundamentals were also underscored by other data on Thursday showing a solid increase in construction spending in December. A drop in worker productivity in the fourth quarter, however, suggested it may be hard to maintain the strong pace of economic growth.

The Institute for Supply Management (ISM) said its index of national factory activity fell to a reading of 59.1 last month from 59.3 in December. A reading above 50 in the ISM index indicates growth in manufacturing, which accounts for about 12 percent of the U.S. economy.

The survey's production sub-index slipped 0.7 points to a reading of 64.5 in January and a measure of factory employment fell 3.9 points to 54.2. A gauge of new orders declined to 65.4 last month from 67.4 in December.

The moderation in orders is likely to be temporary against the backdrop of strong domestic and global demand. Manufacturers reported an increase in export orders.

Domestic demand increased at its fastest pace in more than three years in the fourth quarter. A weak dollar, which fell 7 percent against the currencies of the United States' main trading partners last year, is making U.S.-made goods more competitive on the international market.

Prices of U.S. Treasuries were mixed after the data while U.S. stock indexes were largely flat. The dollar dipped against a basket of currencies.

In a separate report the Labor Department said initial claims for state unemployment benefits slipped 1,000 to a seasonally adjusted 230,000 for the week ended Jan. 27. Economists polled by Reuters had forecast claims rising to 238,000 in the latest week.

Last week marked the 152nd straight week that claims remained below the 300,000 threshold, which is associated with a strong labor market. That is the longest such stretch since 1970, when the labor market was much smaller.

"The untapped reservoir of unemployed or underemployed skilled workers that existed in the aftermath of the recession has largely disappeared," said Jim Baird, chief investment officer at Plante Moran Financial Advisors in Kalamazoo, Michigan. "Employers are finding it more difficult to find potential workers."

NEAR FULL EMPLOYMENT

The labor market is near full employment, with the jobless rate at a 17-year low of 4.1 percent. A tightening of labor market conditions has raised optimism among Federal Reserve officials that inflation will rise towards the U.S. central bank's 2 percent target this year.

The Fed on Wednesday left its benchmark overnight interest rate unchanged and described the job market as having "continued to strengthen." U.S. financial markets expect a rate increase in March. The Fed has forecast three rate increases for this year after lifting borrowing costs three times in 2017.

The claims data has no bearing on January's employment report, which is scheduled to be released on Friday, as it falls outside the survey period. According to a Reuters survey of economists, nonfarm payrolls probably rose by 180,000 jobs in January after increasing by 148,000 in December.

Skilled worker shortages and weak productivity could put pressure on companies seeking to expand their businesses, economists say. That could result in companies investing in automation to increase efficiency and output, according to Plante Moran Financial Advisors' Baird.

In a third report on Thursday, the Labor Department said nonfarm productivity, which measures hourly output per worker, fell at a 0.1 percent annualized rate in the fourth quarter. That was the first drop and weakest performance since the first quarter of 2016.

Third-quarter productivity was revised to show it rising at a pace of 2.7 percent instead of the previously reported 3.0 percent rate. Compared to the fourth quarter of 2016, productivity increased at a rate of 1.1 percent.

Productivity growth averaged 1.2 percent between 2007 and 2017, below its long-term rate of 2.1 percent from 1947 to 2017.

Weak productivity could be an obstacle to faster economic growth. The Trump administration has slashed income taxes as it seeks to lift annual economic growth to 3.0 percent, a figure that has not been surpassed since 2005. Gross domestic product rose 2.3 percent in 2017.

Unit labor costs, the price of labor per single unit of output, rose at a pace of 2.0 percent in the final three months of 2017 after slipping at a rate of 0.1 percent in the third quarter. Compared to the fourth quarter of 2016, unit labor costs rose at a rate of 1.3 percent.

They gained 0.2 percent in 2017, the smallest increase since 2010, after rising 1.1 percent in 2016.

A fourth report from the Commerce Department on Thursday showed construction spending rose 0.7 percent to an all-time high of $1.25 trillion. It advanced 2.6 percent on a year-on-year basis.

In December, spending on private construction projects rose 0.8 percent to a record high of $963.2 billion after increasing 0.7 percent in November. Outlays on private residential projects gained 0.5 percent to the highest level since March 2007, after surging 1.1 percent in November. (Reporting by Lucia Mutikani; Editing by Paul Simao)